Cannon–Thurston maps for hyperbolic free group extensions

Cannon–thurston Maps for Hyperbolic Free Group Extensions

This paper gives a detailed analysis of the Cannon–Thurston maps associated to a general class of hyperbolic free group extensions. Let F denote a free groups of finite rank at least 3 and consider a convex cocompact subgroup Γ ≤ Out(F), i.e. one for which the orbit map from Γ into the free factor complex of F is a quasi-isometric embedding. The subgroup Γ determines an extension EΓ of F, and t...

Hyperbolic extensions of free groups

Given a finitely generated subgroup Γ≤ Out(F) of the outer automorphism group of the rank r free group F = Fr, there is a corresponding free group extension 1→ F→ EΓ→ Γ→ 1. We give sufficient conditions for when the extension EΓ is hyperbolic. In particular, we show that if all infinite order elements of Γ are atoroidal and the action of Γ on the free factor complex of F has a quasi-isometric o...

Livsiĉ Theory for Compact Group Extensions of Hyperbolic Systems

We prove Livsiĉ type results for rapidly mixing compact group extensions of Anosov diffeomorphisms.

Group Extensions of Gibbs-markov Maps

Relative Hyperbolic Extensions of Groups and Cannon-thurston Maps

Let 1 → (K, K1) → (G, NG(K1)) → (Q, Q1) → 1 be a short exact sequence of pairs of finitely generated groups with K strongly hyperbolic relative to the subgroup K1. Let relative hyperbolic boundary of K with respect to K1 contains atleast three distinct parabolic end points and for all g ∈ G there exists k ∈ K such that gK1g −1 = kK1k , then we prove that there exists a quasi-isometric section s...